cantors-attic

Climb into Cantor’s Attic, where you will find infinities large and small. We aim to provide a comprehensive resource of information about all notions of mathematical infinity.

View the Project on GitHub neugierde/cantors-attic

Quick navigation
The upper attic
The middle attic
The lower attic
The parlour
The playroom
The library
The cellar

Sources
Cantor's Attic (original site)
Joel David Hamkins blog post about the Attic
Latest working snapshot at the wayback machine

The small countable ordinals

The ordinals begin with the following transfinite progression

$0,1,2,3,\ldots,\omega,\omega+1,\omega+2,\omega+3,\ldots,\omega\cdot 2,\omega\cdot 2+1,\ldots,\omega\cdot 3,\ldots,\omega^2,\omega^2+1,\ldots,\omega^2+\omega,\ldots,\omega^2+\omega+1,\ldots,\omega^2+\omega\cdot 2,\ldots,\omega^3,\ldots,$

$\omega^\omega,\omega^\omega+1,\ldots,\omega^\omega+\omega,\ldots,\omega^\omega+\omega\cdot 2,\ldots,\omega^\omega\cdot 2,\ldots,\omega^{\omega^\omega},\ldots,\omega^{\omega^{\omega^\omega}},\ldots,\epsilon_{0}$

Counting to $\omega^2$

We explain here in detail how to count to $\omega^2$. This is something that anyone can learn to do, even young children.

The ordinals below $\epsilon_0$

We shall give here an account of the attractive finitary represenation of the ordinals below $\epsilon_0$.